{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A study on spontaneous decay rate of an atom in presence of a square dielectric waveguide using BEM approach\n",
    "\n",
    "In these notes, I calculate the Local Density of States (LDOS), or the imaginary part of the on-site Green's function and hence the modified spontaneous emission rate of an atom in presence of a square dielectric waveguide using the Boundary Element Method (BEM). The BEM code is from Prof. Alejandro Manjavacas's group. \n",
    "\n",
    "This is an [IJulia notebook](https://github.com/JuliaLang/IJulia.jl), which provides a nice\n",
    "browser-based [Jupyter](http://jupyter.org/) interface to the [Julia language](http://julialang.org/), a high-level dynamic language (similar to Matlab or Python+SciPy) for technical computing.  The notebook allows us to combine code and results in one place.\n",
    "\n",
    "We are only manipulating the generated data from the simulation results in this notebook. As a brief recap of the simulation process, I have used a compiled BEM code by Alejandro's group written in C++ called `bem2D` on a cluster computing system. A configuration C++ code is defined in the file `scripts_ldos.cpp` which is in the same folder as `bem2D`. I compiled the script and put the generated executable into another folder called `p3`, for example, by\n",
    "```\n",
    "g++ scripts_ldos.cpp -lstdc++ -o ../p3/scripts_ldos\n",
    "```\n",
    "Then ran the executable and submitted the generated PBS script to the cluster system to run the simulation:\n",
    "```\n",
    "cd ../p3/\n",
    "./scripts_ldos\n",
    "qsub ldos_N_1_lam_894_eps_4_0_a_300_b_300_c_5_x_0_y_350_q_0_2_401.pbs\n",
    "```\n",
    "Notice that the name of the PBS script is automatically generated based on the configuration parameters for this simulation. The name will vary for different simulations. After running the script, I got a set of data files--one has the same name as the PBS script but with a `.dat` extension for the data table storing the calculated LDOS values; there are another two `*.dat` files for the geometry of boundary and dieletric function distribution. We will look into those data files in the following sections.\n",
    "\n",
    "\n",
    "## 3D dielectric waveguide simulated in 2D\n",
    "\n",
    "Just a little more detail on the simulation itself: By assuming the waveguide along z-axis or the light propagation direction is uniform, one can completely solve the boundary condition problem of dipole emission by simulating the field in one single layer of the xy cross section. The z-component of the field only adds in a phase factor. The data of the simulated result is stored in the /data/ folder of this repo. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can read in this data as a matrix of numbers by the `readdlm` function in Julia with the `header=false` option meaning that it reads the first line as the beginning of the data entries without a list of strings describing each column."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's plot the results.  I'll use the [PyPlot](https://github.com/stevengj/PyPlot.jl) package in Julia, which is an interface to the sophisticated [matplotlib](http://matplotlib.org/) Python plotting library.   We'll plot three things:\n",
    "\n",
    "* The waveguide structure in terms of $\\epsilon$ and the interface boundary between two media.\n",
    "* Plot the LDOS components for a fixed dipole position.\n",
    "* Calculate the waveguide-modified spontaneous decay rate when the dipole varies its position outside of the waveguide.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the boundary and index of refraction profile of the waveguide in the xy cross section\n",
    "\n",
    "Our boundary points are meshed in the file `/data/p3/geom_regions_a_300_b_300_c_5.data`, which positions where the equivalent charges and current sources to be computed in the BEM simulation. The waveguide has a square cross-section of a width $a=b=300nm$ ($nm$ is the unit of length) and a index of refraction of $n_1=n_{core}=2$ for the waveguide material and $n_2=n_{clad}=1$ for the vacuum clad. \n",
    "\n",
    "It is good to plot out the mesh of index of refraction in space and find out how good is the mesh resolution. This can be done by plotting out the output eps file in a simple data table format, which ends in `.dat`. \n",
    "\n",
    "The following will first print out some of the data in order to figure out the physics meaning of the dimensions. They should contain the coordinate and index of refraction information for the simulation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another set of data is taken at $r=330nm$ position with a slightly different setting--mainly the edges are having a larger radius. We can plot the result below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "As plotted below, the dipole is changing position from $225$nm to $420$nm from the origin (center of the waveguide) along the x-axis. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The guide mode contribution seems very small compared to the nanofiber case using the BEM approach. As discussed in other tests, the BEM calculation on the guided mode contribution part is not accurate due to the fact that the dielectric function has a zero imaginary part or loss in the frequency domain which will cause an infinite narrow peak of the LDOS function and leads to unphysical solution. \n",
    "To avoid this difficulty, we will use other method to calculate the guided mode contribution part to the Green's function tensor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculation of Green's function tensor using BEM\n",
    "\n",
    "BEM can output full local field components so that computing the radiative mode contribution to the full Green's function tensor is possible. With the Green's function tensor, one can then calculate the modified decay rates with dipoles orientated along arbitrary directions--including the dipole transitions corresponding to $\\sigma_\\pm$ and $\\pi$ transitions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f10793b64d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load data for different dipole positions.\n",
    "rp_BEM=160:10:600;#[170,190,210,230,250,270,290,310,330,350,370,390,410,430,450,470];\n",
    "lenrp=length(rp_BEM);\n",
    "lendr=201;\n",
    "E_dipolex = readdlm(\"data/D2/dipolex_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_330_y_0_q_0_2_201.dat\", header=false);\n",
    "k_vec=E_dipolex[:,2];\n",
    "Ex_dx=zeros(Complex{Float64},lendr,lenrp); Ey_dx=zeros(Complex{Float64},lendr,lenrp); Ez_dx=zeros(Complex{Float64},lendr,lenrp);\n",
    "Ex_dy=zeros(Complex{Float64},lendr,lenrp); Ey_dy=zeros(Complex{Float64},lendr,lenrp); Ez_dy=zeros(Complex{Float64},lendr,lenrp);\n",
    "Ex_dz=zeros(Complex{Float64},lendr,lenrp); Ey_dz=zeros(Complex{Float64},lendr,lenrp); Ez_dz=zeros(Complex{Float64},lendr,lenrp);\n",
    "for ii=2:2:(lenrp-1)\n",
    "    E_dipolex = readdlm(\"data/D2/dipolex_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_$(rp_BEM[ii])_y_0_q_0_2_201.dat\", header=false); #\",rp_list[ii],\"\n",
    "    Ex_dx[:,ii]=E_dipolex[:,5]+im*E_dipolex[:,6];\n",
    "    Ey_dx[:,ii]=E_dipolex[:,7]+im*E_dipolex[:,8];\n",
    "    Ez_dx[:,ii]=E_dipolex[:,9]+im*E_dipolex[:,10];\n",
    "    \n",
    "    E_dipoley = readdlm(\"data/D2/dipoley_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_$(rp_BEM[ii])_y_0_q_0_2_201.dat\", header=false); #\",rp_list[ii],\"\n",
    "    Ex_dy[:,ii]=E_dipoley[:,5]+im*E_dipoley[:,6];\n",
    "    Ey_dy[:,ii]=E_dipoley[:,7]+im*E_dipoley[:,8];\n",
    "    Ez_dy[:,ii]=E_dipoley[:,9]+im*E_dipoley[:,10];\n",
    "    \n",
    "    E_dipolez = readdlm(\"data/D2/dipolez_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_$(rp_BEM[ii])_y_0_q_0_2_201.dat\", header=false); #\",rp_list[ii],\"\n",
    "    Ex_dz[:,ii]=E_dipolez[:,5]+im*E_dipolez[:,6];\n",
    "    Ey_dz[:,ii]=E_dipolez[:,7]+im*E_dipolez[:,8];\n",
    "    Ez_dz[:,ii]=E_dipolez[:,9]+im*E_dipolez[:,10];\n",
    "end\n",
    "for ii=1:2:lenrp\n",
    "    E_dipolex = readdlm(\"data/D2/dipolex_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_$(rp_BEM[ii])_y_0_q_0_2_201.dat\", header=false); #\",rp_list[ii],\"\n",
    "    Ex_dx[:,ii]=E_dipolex[:,5]+im*E_dipolex[:,6];\n",
    "    Ey_dx[:,ii]=E_dipolex[:,7]+im*E_dipolex[:,8];\n",
    "    Ez_dx[:,ii]=E_dipolex[:,9]+im*E_dipolex[:,10];\n",
    "    \n",
    "    E_dipoley = readdlm(\"data/D2/dipoley_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_$(rp_BEM[ii])_y_0_q_0_2_201.dat\", header=false); #\",rp_list[ii],\"\n",
    "    Ex_dy[:,ii]=E_dipoley[:,5]+im*E_dipoley[:,6];\n",
    "    Ey_dy[:,ii]=E_dipoley[:,7]+im*E_dipoley[:,8];\n",
    "    Ez_dy[:,ii]=E_dipoley[:,9]+im*E_dipoley[:,10];\n",
    "    \n",
    "    E_dipolez = readdlm(\"data/D2/dipolez_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_$(rp_BEM[ii])_y_0_q_0_2_201.dat\", header=false); #\",rp_list[ii],\"\n",
    "    Ex_dz[:,ii]=E_dipolez[:,5]+im*E_dipolez[:,6];\n",
    "    Ey_dz[:,ii]=E_dipolez[:,7]+im*E_dipolez[:,8];\n",
    "    Ez_dz[:,ii]=E_dipolez[:,9]+im*E_dipolez[:,10];\n",
    "end\n",
    "# Calculate the diagonal elements of the Green's function tensor from the radiation mode contribution.\n",
    "c=2.99792458e8;\n",
    "au=1.72e7; # This is the atomic unit in the CGS-units: $q/a_0^2$ statvolts/cm. In SI units, it becomes $e/(4π\\varepsilon_0a_0^2)$ = 5.2e11 V/m.\n",
    "lambda0=0.895e-6;\n",
    "ω=2.*pi*c/lambda0;\n",
    "GFT_rad_ind=zeros(Complex{Float64},3,3,lenrp);\n",
    "Gxx_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gxy_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gxz_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gyx_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gyy_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gyz_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gzx_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gzy_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gzz_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "G0=Inf + 2.0/3.*(ω/c)^3*im;\n",
    "gamma_rad_BEM_rp_average=zeros(lenrp);\n",
    "gamma_rad_BEM_rp_sigmap=zeros(lenrp);\n",
    "gamma_rad_BEM_rp_sigmam=zeros(lenrp);\n",
    "gamma_rad_BEM_rp_pi=zeros(lenrp);\n",
    "# Define the unitary dipole orientation vector.\n",
    "e_dipole_sigmap=[-1.;-1.0*im;0]/sqrt(2);\n",
    "e_dipole_sigmam=[1.; -1.0*im;0]/sqrt(2);\n",
    "e_dipole_pi=[0.; 0.; 1.];\n",
    "breakpoint=100; # The index of k vector to cut off for the radiative mode in the range of [0,1]k_0.\n",
    "using NumericalIntegration\n",
    "for ii=1:lenrp\n",
    "    Gxx_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ex_dx[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;#G0+\n",
    "    Gyy_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ey_dy[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;#G0+\n",
    "    Gzz_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ez_dz[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;#G0+\n",
    "    Gyx_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ey_dx[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gzx_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ez_dx[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gxy_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ex_dy[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gzy_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ez_dy[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gxz_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ex_dz[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gyz_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ey_dz[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    GFT_rad_ind[:,:,ii]=[Gxx_rad_ind[ii] Gxy_rad_ind[ii] Gxz_rad_ind[ii];\n",
    "        Gyx_rad_ind[ii] Gyy_rad_ind[ii] Gzy_rad_ind[ii];\n",
    "        Gzx_rad_ind[ii] Gzy_rad_ind[ii] Gzz_rad_ind[ii]];\n",
    "end\n",
    "\n",
    "# Calculate the relative averaged decay rate at the given dipole located at x=405nm and y=0.\n",
    "gamma0=imag(G0);\n",
    "for ii =1:lenrp\n",
    "    gamma_rad_BEM_rp_average[ii]=1+trace(imag(GFT_rad_ind[:,:,ii]))/gamma0/3.;\n",
    "    gamma_rad_BEM_rp_sigmap[ii]=1+real((e_dipole_sigmap'*imag(GFT_rad_ind[:,:,ii])*e_dipole_sigmap)/gamma0)[1];\n",
    "    gamma_rad_BEM_rp_sigmam[ii]=1+real((e_dipole_sigmam'*imag(GFT_rad_ind[:,:,ii])*e_dipole_sigmam)/gamma0)[1];\n",
    "    gamma_rad_BEM_rp_pi[ii]=1+real((e_dipole_pi'*imag(GFT_rad_ind[:,:,ii])*e_dipole_pi)/gamma0)[1];\n",
    "end\n",
    "\n",
    "# Recalculate the diagonal GFT elements with a dipole placed at r'=405nm from the fiber axis with lower imaginary part of epsilon.\n",
    "E_dipolex = readdlm(join([\"data/D2/dipolex_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_\",\"330\",\"_y_0_q_0_2_201.dat\"]), header=false)\n",
    "Ex_dx_r0=E_dipolex[:,5]+im*E_dipolex[:,6];\n",
    "Ey_dx_r0=E_dipolex[:,7]+im*E_dipolex[:,8];\n",
    "Ez_dx_r0=E_dipolex[:,9]+im*E_dipolex[:,10];\n",
    "E_dipoley = readdlm(join([\"data/D2/dipoley_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_\",\"330\",\"_y_0_q_0_2_201.dat\"]), header=false)\n",
    "Ex_dy_r0=E_dipoley[:,5]+im*E_dipoley[:,6];\n",
    "Ey_dy_r0=E_dipoley[:,7]+im*E_dipoley[:,8];\n",
    "Ez_dy_r0=E_dipoley[:,9]+im*E_dipoley[:,10];\n",
    "E_dipolez = readdlm(join([\"data/D2/dipolez_E_N_1_lam_852_eps_4_0.001_a_300_b_300_c_6_x_\",\"330\",\"_y_0_q_0_2_201.dat\"]), header=false)\n",
    "Ex_dz_r0=E_dipolez[:,5]+im*E_dipolez[:,6];\n",
    "Ey_dz_r0=E_dipolez[:,7]+im*E_dipolez[:,8];\n",
    "Ez_dz_r0=E_dipolez[:,9]+im*E_dipolez[:,10];\n",
    "Gxx_rad_r0=integrate(k_vec[1:breakpoint],Ex_dx_r0[1:breakpoint],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "Gyy_rad_r0=integrate(k_vec[1:breakpoint],Ey_dy_r0[1:breakpoint],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "Gzz_rad_r0=integrate(k_vec[1:breakpoint],Ez_dz_r0[1:breakpoint],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "gamma_rad_BEM_r0=imag(Gxx_rad_r0+Gyy_rad_r0+Gzz_rad_r0)/3/gamma0;\n",
    "\n",
    "# Plot out gamma_rad as a function of dipole position.\n",
    "using PyPlot\n",
    "figure(figsize=(16,3));\n",
    "subplot(1,2,1)\n",
    "plot((1:breakpoint)/100.,real(Ex_dx[1:breakpoint,4]),\"r-\")\n",
    "plot((1:breakpoint)/100.,imag(Ex_dx[1:breakpoint,4]),\"b-\")\n",
    "ylabel(L\"E(\\beta)\")\n",
    "xlabel(L\"\\beta/k_0\")\n",
    "legend([\"Real\",\"Imag\"],loc=\"upper left\")\n",
    "\n",
    "subplot(1,2,2)\n",
    "a=300.;\n",
    "#plot(rp0_test[1,:]/1.e-9, 1+sum(gamma_rad,2), \"r-\", linewidth=2.0)\n",
    "plot(rp_BEM-a/2,real(gamma_rad_BEM_rp_average),\"b-\");\n",
    "plot(330-a/2,real(gamma_rad_BEM_r0)+1.,\"mo\");\n",
    "plot(rp_BEM-a/2,gamma_rad_BEM_rp_sigmap,\"r--\");\n",
    "plot(rp_BEM-a/2,gamma_rad_BEM_rp_sigmam,\"m.-\");\n",
    "plot(rp_BEM-a/2,gamma_rad_BEM_rp_pi,\"k.\");\n",
    "xlabel(\"(r'-a/2)/nm\");\n",
    "ylabel(L\"\\Gamma_{rad}^{BEM}/\\Gamma_0\");\n",
    "#ylim([0,1.2])\n",
    "legend([\"average\",L\"average_{no\\,\\,loss}\",L\"\\sigma_+\",L\"\\sigma_-\",L\"\\pi\"],loc=\"upper right\",fontsize=12);\n",
    "#gamma_rad_BEM_rp_sigmap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The first figure (on the left) shows the real and imaginary parts of the $E_x$ component changes as a function of $\\beta=k_z$ in the radiative mode regime.\n",
    "\n",
    "The second figure (on the right) shows the decay rates caused by non-guided modes and decomposed into the $\\sigma_\\pm$ and $\\pi$ transitions and their average.\n",
    "In calculating the averaged non-guided mode induced decay rates, we define\n",
    "$$\\begin{align}\n",
    "\\frac{\\Gamma_{rad}^{ave}}{\\Gamma_0} &= 1+ \\frac{\\sum_{i=x,y,z}\\mathrm{Im}\\left[\\mathbf{e}_i^*\\cdot \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_i\\right]}{\\sum_{i=x,y,z} \\mathrm{Im}\\left[\\mathbf{e}_i^*\\cdot \\mathbf{G}_0(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_i\\right]}\\\\\n",
    "&=1+ \\frac{\\sum_{i=x,y,z}\\mathrm{Im}\\left[\\mathbf{e}_i^*\\cdot \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_i\\right]}{3\\mathrm{Im}\\left[G_0(\\mathbf{r}',\\mathbf{r}')\\right]}\\\\\n",
    "&= 1+ \\frac{\\mathrm{Tr}\\left\\{\\mathrm{Im}\\left[ \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\right]\\right\\}}{3\\mathrm{Im}\\left[G_0(\\mathbf{r}',\\mathbf{r}')\\right]}\n",
    "\\end{align}$$\n",
    "with the free-space Green's function scaled by $G_0(\\mathbf{r}',\\mathbf{r}';\\omega)=\\frac{2}{3}k_0^3$ in the CGS units as $\\mathbf{G}_0=G_0\\mathbb{1}$ and the numerical result of the waveguide-induced Green's function tensor elements\n",
    "$$ G_{ind,rad}^{ij}(\\mathbf{r}',\\mathbf{r}')=\\frac{2k_0^2*a.u.}{3\\pi^2}\\int_{-k_0}^{k_0} d\\beta E_j^i(\\mathbf{r}')=\\frac{4k_0^2*a.u.}{3\\pi^2}\\int_{0}^{k_0} d\\beta E_j^i(\\mathbf{r}')$$\n",
    "calculated via BEM by putting a unit dipole in atomic units orientated along $j$ direction while the $i$-th electric field component is measured at the dipole position.\n",
    "We have used $\\varepsilon=4+0.01i$ (with a small loss) and $\\varepsilon=4$ (without loss) to calculate the Green's function tensors as well as the averaged corresponding decay rate contributions.\n",
    "These two cases doesn't show a noticeable difference with one sampling data point as shown in the purple dot points. \n",
    "\n",
    "In calculating the corresponding contributions from the $\\sigma_\\pm$ and $\\pi$ transitions of the atoms, we have defined\n",
    "$$\\begin{align}\n",
    "\\frac{\\Gamma_{rad}^{\\mathbf{e}_q}}{\\Gamma_0} &= 1+ \\frac{\\mathrm{Im}\\left[\\mathbf{e}_q^*\\cdot \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_q\\right]}{ \\mathrm{Im}\\left[\\mathbf{e}_q^*\\cdot \\mathbf{G}_0(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_q\\right]}\n",
    "=1+ \\frac{\\mathrm{Im}\\left[\\mathbf{e}_q^*\\cdot \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_q\\right]}{\\mathrm{Im}\\left[G_0(\\mathbf{r}',\\mathbf{r}')\\right]},\n",
    "\\end{align}$$\n",
    "where the three orthogonal dipole transition bases\n",
    "$$\\begin{align}\n",
    "\\mathbf{e}_\\pm &=\\mp \\frac{\\mathbf{e}_{\\tilde{x}}\\pm i\\mathbf{e}_{\\tilde{y}}}{\\sqrt{2}}\\\\\n",
    "\\mathbf{e}_0 &=\\mathbf{e}_{\\tilde{z}}\n",
    "\\end{align}$$\n",
    "correspond to the $\\sigma_\\pm$ and $\\pi$ transitions of the atoms.\n",
    "These basis vectors are quantization-axis dependent, but in our calculation above, we assume the $z$-axis or the waveguide axis is the quantization axis, and hence $\\mathbf{e}_{\\tilde{x}}=\\mathbf{e}_x$, $\\mathbf{e}_{\\tilde{y}}=\\mathbf{e}_y$ and $\\mathbf{e}_{\\tilde{z}}=\\mathbf{e}_z$. \n",
    "\n",
    "As you can see, when the atoms are placed around $200$nm from the nanofiber surface, different dipole transitions make a noticeable difference.\n",
    "\n",
    "To wrap up, the total decay rates\n",
    "$$\\begin{align}\n",
    "\\Gamma \\propto \\mathbf{e}_d^*\\cdot \\mathrm{Im}\\left[\\mathbf{G}(\\mathbf{r}',\\mathbf{r}')\\right]\\cdot \\mathbf{e}_d,\n",
    "\\end{align}$$\n",
    "where $$\\mathbf{G}=\\mathbf{G}_{hom}+\\mathbf{G}_{inhom}=\\mathbf{G}_{rad,free-space}+\\mathbf{G}_{rad,ind}+\\mathbf{G}_{gyd}$$\n",
    "with $\\mathbf{G}_{rad,free-space}=\\mathbf{G}_0$ and $\\mathrm{Im}\\left[ \\mathbf{G}_0(\\mathbf{r}',\\mathbf{r}')\\right]=\\frac{2}{3}\\mathbb{1}$.\n",
    "In the end, the total decay rate\n",
    "$$\\begin{align}\\Gamma = \\Gamma_{rad}+\\Gamma_{gyd}=\\Gamma_{rad,free-space}+\\Gamma_{rad,ind}+\\Gamma_{gyd}\\end{align}$$\n",
    "with $\\Gamma_{rad,free-space}=\\Gamma_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Export data to a MAT file.\n",
    "using MAT\n",
    "matopen(\"data/D2/Julia_swg_GFT_decayrates_rad_D2.mat\", \"w\") do matfile\n",
    "    write(matfile,\"omega0\",ω)\n",
    "    write(matfile,\"rp_BEM\",collect(rp_BEM))\n",
    "    write(matfile,\"gamma0\",gamma0)\n",
    "    write(matfile,\"e_dipole_sigmap\",e_dipole_sigmap)\n",
    "    write(matfile,\"e_dipole_sigmam\",e_dipole_sigmam)\n",
    "    write(matfile,\"e_dipole_pi\",e_dipole_pi)\n",
    "    write(matfile,\"gamma_rad_BEM_rp_average\",gamma_rad_BEM_rp_average)\n",
    "    write(matfile,\"gamma_rad_BEM_rp_sigmap\",gamma_rad_BEM_rp_sigmap)\n",
    "    write(matfile,\"gamma_rad_BEM_rp_sigmam\",gamma_rad_BEM_rp_sigmam)\n",
    "    write(matfile,\"gamma_rad_BEM_rp_pi\",gamma_rad_BEM_rp_pi)\n",
    "    write(matfile,\"a\",a)\n",
    "    write(matfile,\"GFT_rad_rp\",GFT_rad_ind)\n",
    "    write(matfile,\"Gxx_rad_rp\",Gxx_rad_ind)\n",
    "    write(matfile,\"Gxy_rad_rp\",Gxy_rad_ind)\n",
    "    write(matfile,\"Gxz_rad_rp\",Gxz_rad_ind)\n",
    "    write(matfile,\"Gyx_rad_rp\",Gyx_rad_ind)\n",
    "    write(matfile,\"Gyy_rad_rp\",Gyy_rad_ind)\n",
    "    write(matfile,\"Gyz_rad_rp\",Gyz_rad_ind)\n",
    "    write(matfile,\"Gzx_rad_rp\",Gzx_rad_ind)\n",
    "    write(matfile,\"Gzy_rad_rp\",Gzy_rad_ind)\n",
    "    write(matfile,\"Gzz_rad_rp\",Gzz_rad_ind)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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